Preheat oven to 375°F and generously mist a 9-inch glass or ceramic pie dish with cooking spray.
Combine spaghetti, mozzarella and Swiss cheese in a large bowl. Add scallions and toss to blend. In a small bowl, beat eggs with milk until blended. Pour over spaghetti, season with 1/2 tsp. salt and 1/4 tsp. pepper, mix well and pour into baking dish.
Combine panko and Parmesan in a small bowl. Add melted butter; toss with a fork to coat crumbs. Spread evenly over top of spaghetti mixture and bake until golden brown on top, about 25 minutes. Let stand for 5 minutes. Cut into wedges and serve.